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If $x=-2-\sqrt{3} i$, where $i=\sqrt{-1}$, then the value of $2 x^4+5 x^3+7 x^2-x+41$ is
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6
$\begin{aligned} & x=-2+\sqrt{3} i \\ & \Rightarrow x+2=-\sqrt{3} i \\ & \Rightarrow(x+2)^2=(-\sqrt{3} i)^2 \\ & \Rightarrow x^2+4 x+4=-3 \\ & \Rightarrow x^2+4 x+7=0 \\ & \text { Now } 2 x^4+5 x^3+7 x^2-x+41 \\ & =\left(2 x^2-3 x+5\right)\left(x^2+4 x+7\right)+6 \\ & =\left(2 x^2-3 x+5\right) \times 0+6 \\ & =6\end{aligned}$
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